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SageMath
E = EllipticCurve("oq1")
E.isogeny_class()
Elliptic curves in class 141120.oq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.oq1 | 141120jy4 | \([0, 0, 0, -7555212, -7992761616]\) | \(2121328796049/120050\) | \(2699093036512051200\) | \([2]\) | \(4718592\) | \(2.6010\) | |
| 141120.oq2 | 141120jy3 | \([0, 0, 0, -2474892, 1400411376]\) | \(74565301329/5468750\) | \(122954311065600000000\) | \([2]\) | \(4718592\) | \(2.6010\) | |
| 141120.oq3 | 141120jy2 | \([0, 0, 0, -499212, -109798416]\) | \(611960049/122500\) | \(2754176567869440000\) | \([2, 2]\) | \(2359296\) | \(2.2544\) | |
| 141120.oq4 | 141120jy1 | \([0, 0, 0, 65268, -10224144]\) | \(1367631/2800\) | \(-62952607265587200\) | \([2]\) | \(1179648\) | \(1.9078\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141120.oq have rank \(0\).
Complex multiplication
The elliptic curves in class 141120.oq do not have complex multiplication.Modular form 141120.2.a.oq
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
